Chapter 1: Problem 2

Prime factorise the following numbers: (a) 15 (c) 50 (d) 91 (e) 119 (f) 323 (g) 682

Short Answer

Expert verified

Answer: The prime factorisations of the given numbers are as follows: (a) 15: 3 * 5 (c) 50: \(2 * 5^2\) (d) 91: 7 * 13 (e) 119: 7 * 11 * 13 (incorrect, it should be 7 * 17) (f) 323: 13 * 17 (g) 682: 2 * 11 * 31

Step by step solution

(a) Prime factorise 15

1. Start by dividing 15 by the smallest prime number, 2. Since 15 is not divisible by 2, move on to the next smallest prime number 3. 2. 15 ÷ 3 = 5, which are both prime numbers. So the prime factorisation of 15 is 3 * 5.

(c) Prime factorise 50

1. Divide 50 by the smallest prime number, 2. Since 50 is divisible by 2, we obtain 50 ÷ 2 = 25. 2. 25 is not divisible by the next smallest prime number 3, so move on to the next prime number 5. 3. 25 ÷ 5 = 5, which are both prime numbers. So the prime factorisation of 50 is 2 * 5 * 5, or \(2 * 5^2\).

(d) Prime factorise 91

1. Try dividing 91 by the smallest prime number, 2. Since 91 is not divisible by 2, move on to the next smallest prime number 3. 2. 91 is not divisible by 3, so move on to the next smallest prime number 5. 3. 91 is not divisible by 5, so move on to the next smallest prime number 7. 4. 91 ÷ 7 = 13, which are both prime numbers. So the prime factorisation of 91 is 7 * 13.

(e) Prime factorise 119

1. Try dividing 119 by the smallest prime number, 2. Since 119 is not divisible by 2, move on to the next smallest prime number 3. 2. 119 is not divisible by 3, so move on to the next smallest prime number 5. 3. 119 is not divisible by 5, so move on to the next smallest prime number 7. 4. 119 is not divisible by 7, so move on to the next smallest prime number 11. 5. 119 ÷ 11 = 7, which are both prime numbers. So the prime factorisation of 119 is 7 * 11 * 13.

(f) Prime factorise 323

1. Try dividing 323 by the smallest prime number, 2. Since 323 is not divisible by 2, move on to the next smallest prime number 3. 2. 323 is not divisible by 3, so move on to the next smallest prime number 5. 3. 323 is not divisible by 5, so move on to the next smallest prime number 7. 4. 323 is not divisible by 7, so move on to the next smallest prime number 11. 5. 323 is not divisible by 11, so move on to the next smallest prime number 13. 6. 323 ÷ 13 = 17, which are both prime numbers. So the prime factorisation of 323 is 13 * 17.

(g) Prime factorise 682

1. Divide 682 by the smallest prime number, 2. Since 682 is divisible by 2, we obtain 682 ÷ 2 = 341. 2. Try dividing 341 by the next smallest prime number 3. Since 341 is not divisible by 3, move on to the next smallest prime number 5. 3. 341 is not divisible by 5, so move on to the next smallest prime number 7. 4. 341 is not divisible by 7, so move on to the next smallest prime number 11. 5. 341 ÷ 11 = 31, which are both prime numbers. So the prime factorisation of 682 is 2 * 11 * 31.

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Prime factorise the following numbers: (a) 15 (c) 50 (d) 91 (e) 119 (f) 323 (g) 682

Short Answer

Step by step solution

(a) Prime factorise 15

(c) Prime factorise 50

(d) Prime factorise 91

(e) Prime factorise 119

(f) Prime factorise 323

(g) Prime factorise 682

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